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Question 1010398: What does the line -4x + 3y = -7 look like?
horizontal
vertical
slanted right upwards
slanted right downwards
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52803)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! the equation is -4x + 3y = -7
to get an idea of what it looks like, put it in the form of y = mx + b.
m is the slope and b is the y-intercept.
the slope is the change in the value of y divided by the change in the value of x.
the y-intercept is the value of y when the value of x is 0.
start with -4x + 3y = -7
add 4x to both sides of the equation to get 3y = 4x - 7
divide both sides of the equation by 3 to get y = (4/3)*x - (7/3)
the equation is now in slope intercept form.
the slope is 4/3.
the y-intercept is 7/3.
since the slope is positive, the line is slanting up as it moves to the right.
the y-axis is the vertical line where the value of x is 0.
the x-axis is the horizontal line where the value of y is 0.
the value of y will be -7/3 when the value of x is 0.
this means that the graph of the equation, which is a straight line, will cross the y-axis at the point (0,-7/3).
the graph of the equation of the line is shown below:
from the graph, you can see that the line crosses the y-axis at the point (0,-2 and 1/3).
in decimal form, -2 and 1/3 is shown on the graph as -2.333 rounded to three decimal places.
from the graph, you can see that the point (9,9 and 2/3) is also on the line.
the general form of the coordinates of a point is (x,y).
in the point (9,9 and 2/3):
9 is the x-coordinate of the point.
9 and 2/3 is the y-coordinate of the point.
in decimal form, 9 and 2/3 is shown on the graph as 9.667 rounded to three decimal places.
9 and 2/3 can also be shown as (29/3).
your y-intercept is the value of y when x is 0 which is -2 and 2/3 which is the same as - 7/3 as shown in the equation.
the slope would be calculated from any 2 points on the line.
the formula is m = (y2-y1) / (x2-x1)
(x1,y1) is one point on the line which we'll assign to (0,-7/3).
(x2,y2) is another point on the line which we'll assign to (9,29/3).
the slope is  =  =  =  =  =  .
that's the same as the slope in the equation.
the equation is, once again, y = (4/3)*x - (7/3)
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