Question

Use the given conditions to write an equation for the line in point-slope form and

in slope-intercept form.
Passing through (1,8) with x-intercept 4

Answer 1

`\rm{y=-\cfrac{8}{3}x+\cfrac{32}{3}}`

Explanation:

Given information:

• x-intercept = 4
• point (1,8)

Solving for:

• The line's equation

Notice that we don't have the slope - well, we can find it! The fastest way to find the slope is to use the formula;

`\sf{m=\cfrac{y_2-y_1}{x_2-x_1}}`

Do we have two points? Yes, we do, One of them is the point (4,0), or the x-intercept, and the other point is one that the line passes through, which is (1,8).

So, we find the slope

`\sf{m=\cfrac{8-0}{1-4}}`

`\sf{m=\cfrac{8}{-3}}`

`\sf{m=-\cfrac{8}{3}}`

Now, we know both the slope and the point on the line, so, we plug this information into our point-slope equation:

`\large\boldsymbol{y-y_1=m(x-x_1)}`

Plug in the values:

`\sf{y-8=-\cfrac{8}{3}(x-1)}`

Simplify:

`\sf{y-8=-\cfrac{8}{3}x+\cfrac{8}{3}}`

Add 8 to both sides:

`\sf{y=-\cfrac{8}{3}x+\cfrac{8}{3}+\cfrac{8}{1}}`

`\sf{y=-\cfrac{8}{3}x+\cfrac{8}{3}+\cfrac{24}{3}}`

`\boxed{\boxed{\sf{y=-\cfrac{8}{3}x+\cfrac{32}{3}}}}}`