Question

A line has a slope of $m,$ and its $y$-intercept is $(0,k)$. If $m = -\frac{3}{7}$ and $k = 18,$ then what is the $x$-intercept of the line?

Pls answer it quickly or soon as possible

Answer 1

we can look at this, this way, what's the equation of a line whose slope is -3/7 and it passes through (0 , 18)?

`(\stackrel{x_1}{0}~,~\stackrel{y_1}{18})\hspace{10em} \stackrel{slope}{m} ~=~ -\cfrac{3}{7} \\\\\\ \begin{array} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{18}=\stackrel{m}{-\cfrac{3}{7}}(x-\stackrel{x_1}{0})`

now, what's its x-intercept?

well, to get the x-intercept we simply set "y = 0" and solve for "x".

`\stackrel{y}{0}-18=-\cfrac{3}{7}(x-0)\implies -18=-\cfrac{3x}{7}\implies -126=-3x \\\\\\ \cfrac{-126}{-3}=x\implies 42=x\hspace{5em}\boxed{\stackrel{x-intercept}{(42~~,~~0)}}`

Answer 2

(42, 0)

Explanation:

Given:

`\sf Slope = m = -(3)/(7)`

`\sf Y-intercept = (0, k) = (0, 18)`

Solution:

To find the x-intercept, we can set y to zero and solve for x.

`\sf y = mx + b`

`\sf 0 = mx + b`

`\sf -(3)/(7)x + 18 = 0`

`\sf -(3)/(7)x = -18`

`\sf x = -18\cdot -(7)/(3)`

`\sf x = 42`

Therefore, the x-intercept of the line is (42, 0).