Question

The x-intercept of a line is -5 and the y-intercept of the line is -3. What is the equation of the line?

Answer 1

y = mx + b

y intercept is at (0,-3):-
 -3 = m(0)  + b  so b = -3

x intercept is at (-5,0) so

0 = -5m - 3
m =  -3/5

The equation of the line is y = (-3/5)x - 3   answer

Answer 2

hello!

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since we have the x-intercept of the line, we can just write it as a point:

(-5, 0)

x-intercepts always have a y-coordinate of 0.

now, let's do the same thing with the y-intercept; only note that y-intercepts always have an x-coordinate of 0.

hence, the points are

(-5, 0) and (0, -3)

let's use the points to find the slope:

$\pmb{\displaystyle\frac{y_2-y1}{x2-x1} =\frac{-3-0}{0-(-5)} }}$

simplify:

$\pmb{\displaystyle\frac{-3}{0+5}}$

simplify:

$\pmb{\displaystyle\frac{-3}{5} =-\displaystyle\frac{3}{5} }$

that's the slope; now, we know the y-intercept, so just plug in the values:

$\pmb{y=-\displaystyle\frac{3}{5} x-3}$

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note:-

Hope everything is clear; if you need any more explanation, kindly let me know.