# SOLUTION: Hello out there,I need some help with some slope problems that is giving me a hard time,the first one is,Write the point-slope form of the line that passes through (3,-3)and (5,1).

Algebra ->  Linear-equations -> SOLUTION: Hello out there,I need some help with some slope problems that is giving me a hard time,the first one is,Write the point-slope form of the line that passes through (3,-3)and (5,1).      Log On

Question 82171: Hello out there,I need some help with some slope problems that is giving me a hard time,the first one is,Write the point-slope form of the line that passes through (3,-3)and (5,1).The second one is,Write an equation in slope-intercept form of the line having the given slope and passing through the given point:m=o,(0,-3).The next one is,Write the equation in slope-intercept form of the passing through each pair of points:(6,-2)and (3,-4).The last one is,Write the equation in slope-intercept form of the line passing through each pair of points:(-8,2)and (0,6),thanks for whoever can help.
Answer by jim_thompson5910(33401)   (Show Source):
You can put this solution on YOUR website!
note: if you need more help with finding an equation through 2 points check out this solver

"Write the point-slope form of the line that passes through (3,-3)and (5,1)"

 Solved by pluggable solver: Finding the Equation of a Line First lets find the slope through the points (,) and (,) Start with the slope formula (note: (,) is the first point (,) and (,) is the second point (,)) Plug in ,,, (these are the coordinates of given points) Subtract the terms in the numerator to get . Subtract the terms in the denominator to get Reduce So the slope is ------------------------------------------------ Now let's use the point-slope formula to find the equation of the line: ------Point-Slope Formula------ where is the slope, and (,) is one of the given points So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Rewrite as Distribute Multiply and to get . Now reduce to get Subtract from both sides to isolate y Combine like terms and to get ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line which goes through the points (,) and (,) is: The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver) Graph of through the points (,) and (,) Notice how the two points lie on the line. This graphically verifies our answer.

"The second one is,Write an equation in slope-intercept form of the line having the given slope and passing through the given point:m=0,(0,-3)"

 Solved by pluggable solver: FIND a line by slope and one point What we know about the line whose equation we are trying to find out: it goes through point (0, -3) it has a slope of 0 First, let's draw a diagram of the coordinate system with point (0, -3) plotted with a little blue dot: Write this down: the formula for the equation, given point and intercept a, is (see a paragraph below explaining why this formula is correct) Given that a=0, and , we have the equation of the line: Explanation: Why did we use formula ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (, ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (, ): Here, we know a, , and , and do not know b. It is easy to find out: . So, then, the equation of the line is: . Here's the graph:

note: its hard to see, but its a horizontal line going through (0,-3)

"The next one is,Write the equation in slope-intercept form of the passing through each pair of points:(6,-2)and (3,-4)"

 Solved by pluggable solver: Finding the Equation of a Line First lets find the slope through the points (,) and (,) Start with the slope formula (note: (,) is the first point (,) and (,) is the second point (,)) Plug in ,,, (these are the coordinates of given points) Subtract the terms in the numerator to get . Subtract the terms in the denominator to get Reduce So the slope is ------------------------------------------------ Now let's use the point-slope formula to find the equation of the line: ------Point-Slope Formula------ where is the slope, and (,) is one of the given points So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Rewrite as Distribute Multiply and to get . Now reduce to get Subtract from both sides to isolate y Combine like terms and to get ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line which goes through the points (,) and (,) is: The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver) Graph of through the points (,) and (,) Notice how the two points lie on the line. This graphically verifies our answer.

"Write the equation in slope-intercept form of the line passing through each pair of points:(-8,2)and (0,6)"

 Solved by pluggable solver: Finding the Equation of a Line First lets find the slope through the points (,) and (,) Start with the slope formula (note: (,) is the first point (,) and (,) is the second point (,)) Plug in ,,, (these are the coordinates of given points) Subtract the terms in the numerator to get . Subtract the terms in the denominator to get Reduce So the slope is ------------------------------------------------ Now let's use the point-slope formula to find the equation of the line: ------Point-Slope Formula------ where is the slope, and (,) is one of the given points So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Rewrite as Distribute Multiply and to get . Now reduce to get Add to both sides to isolate y Combine like terms and to get ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line which goes through the points (,) and (,) is: The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver) Graph of through the points (,) and (,) Notice how the two points lie on the line. This graphically verifies our answer.