Question

A line has a slope of $-\frac{3}{7},$ and its $y$-intercept is $(0,18)$. What is its $x$-intercept?

Answer 1

`\text{In order to find your x intercept, plug in 0 to y and solve:}\\\\0=-(3)/(7)x+18\\\\\text{Subtract 18 from both sides}\\\\-18=-(3)/(7)x\\\\\text{Multiply both sides by 7}\\\\-126=-3x\\\\\text{Divide both sides by 3}\\\\42 = x\\\\\text{This means that the x-intercept is (42,0)}\\\\\boxed{\text{x-intercept: (42,0)}}`

Answer 2

(42, 0)

Explanation:

Since we know the slope and y-intercept we can write the equation of the line in slope-intercept form which is y = mx + b; therefore, the equation is y = -3/7x + 18. To find the x-intercept, we just plug in y = 0 which becomes:

0 = -3/7x + 18

-18 = -3/7x

x = 42