SOLUTION: write an equation of a line with a y intercept of "-3" and an x intercept of "-4"

Question 1194153: write an equation of a line with a y intercept of "-3" and an x intercept of "-4"
Found 4 solutions by math_tutor2020, greenestamps, josgarithmetic, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

For linear equations of the form
x/a + y/b = 1
we can quickly spot the x and y intercepts as 'a' and b respectively

In this case, a = -4 and b = -3 to give us
x/a + y/b = 1
x/(-4) + y/(-3) = 1
-x/4 - y/3 = 1

Notice what happens when we plug in x = 0
-x/4 - y/3 = 1
-0/4 - y/3 = 1
0 - y/3 = 1
-y/3 = 1
y = 1(-3)
y = -3
Showing that -3 is the y intercept located at (x,y) = (0,-3)
Through similar steps, you should find y = 0 leads to x = -4 to get the x intercept located at (-4,0)
This confirms we have the correct set up so far.
This example also helps show why x/a + y/b = 1 is useful.

Let's get this equation into slope-intercept form y = mx+b
-x/4 - y/3 = 1
12(-x/4 - y/3) = 12*1
-3x - 4y = 12
-4y = 12+3x
-4y = 3x+12
y = (3x+12)/(-4)
y = 3x/(-4) + 12/(-4)
y = (-3/4)x - 3
In step 2, I multiplied both sides by 12 to clear out the fractions.

The equation y = (-3/4)x - 3 is in y = mx+b form with
m = -3/4 = slope
b = -3 = y intercept

If you need this in standard form Ax+By = C, then,
-x/4 - y/3 = 1
12(-x/4 - y/3) = 12*1
-3x - 4y = 12
-1(-3x - 4y) = -1*12
3x+4y = -12
Some math textbooks require that the x coefficient is positive. This is optional really.
Also, some textbooks may have Ax+By+C = 0 as standard form. So we'd go from 3x+4y = -12 to 3x+4y+12 = 0.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The solution from the other tutor is fine....

When I was a young student, nobody ever talked about the "a/x+b/y=1" form of a linear equation. But you should know it and know how to use it, because it can be useful in particular problems.

But using it is far more work than necessary to answer this question.

If we are looking for an equation in slope-intercept form y=mx+b, we already have the y-intercept: b = -3.

To get the slope m we can use the slope formula with (-4,0) and (0,-3), or we can draw a quick picture on paper or in our mind to see that the slope is -3/4. So

ANSWER: y = (-3/4)x-3

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Points (0,-3) and (-4,0)
means slope is

y-intercept was given, so .
Answer by ikleyn(52784)   (Show Source): You can put this solution on YOUR website!

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