MY question is how can I find the X-intercept, and the Y-intercept of the equation: y - 6 = 4(x + 5)?

Question

I solved what I could like this....

y - 6 = 4(x+5) equals

-6y = 4x + 20

-6 -6 -6

y = -2/3x + 20/6

Slope: -2/3

Y-intercept: (0,20/6)

X-intercept: ?

I cannot remember how to find the X-intercept, once I have gotten to this point.

Could you explain it to me?

I use khan Academy, if that helps.

Thanks for the help!

Answer 1

y-6 = 4(x+5)

is in point slope form, (y-y1) = m(x - 1), where m = slope = 4 and (x1,y1) = (6,-5) is a point on the line

the y-intercept is when x = 0:

y - 6 = 4(0 + 5)

y = 26

the x-intercept is when y = 0:

0 - 6 = 4(x+5)

-6 = 4x + 20

-26 = 4x

-26/4 = x

-13/2 = x

in trying to change the equation to y = mx + b (slope-intercept form), you shouldn't have divided both sides by 6.

y - 6 = 4(x+5)

first distribute right side:

y - 6 = 4x + 20

solve for y by adding 6 to both sides:

y = 4x + 26

so slope is 4 and y-intercept is 26 as solved before.

plug in 0 for y to get -13/2 as x intercept as before