HELP

(1, - 2)   and  (5,10).....we can find the slope  of a line connecttng these points thusly :

[  10 - - 2 ] / [ 5 - 1 ]  =  12 / 4  = 3

The equation of the said line is :

y  = 3 ( x - 5)  + 10

y = 3x - 15 + 10

y = 3x  - 5        where this line crosses the y axis, x  = 0....so

y = 3(0)  - 5   =  0 - 5  =  -5

So.....the line crosses the y axis at  ( 0, - 5)

Here's a graph : https://www.desmos.com/calculator/eearzhfvuk

To answer the question, first figure out the equaton of the line. To do that first find the slope.  The formula for the slope of a line is

$m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$ where m = slope, ${y}_{2}$ = y-coordinate in the second point, ${y}_{1}$ = y-coordinate in the first point, ${x}_{2}$ = x-coordinate in the second point, and ${x}_{1}$ = x-coordintate in the first point.

$m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$

m = ?

${y}_{2}$ = 10

${y}_{1}$ = -2

${x}_{2}$ = 5

${x}_{1}$ = 1

$m=\frac{10-(-2)}{5-1}$

$m=\frac{10+2}{5-1}$

$m=\frac{12}{5-1}$

$m=\frac{12}{4}$

$m=\frac{3}{1}$

$m=3$

Now that we know that the slope of the line is 3, put that in the equation for a line.  The equation for a line is

$y=mx+b$ where $y$ = y-coordinate, $m$ = slope, $x$ = x-coordinate, and $b$ = y intercept (where line crosses the y axis).  Take one of the points and susitute $x$ and $y$ in the equation so we can solve for b.

$y=mx+b$

$y$ = 10

$m$ = 3

$x$ = 5

$b$ = ?

$10=3\times5+b$

$10=15+b$

$10-15=15+b-15$

$-5=15+b-15$

$-5=b-0$

$-5=b$

$b=-5$

Now fill in what you know leaving $y$ and $x$ as $y$ and $x$.

$y=3x-5$

To figure out at which point the line crosses the y-axis, subsitute $x$ for 0 and solve for $x$.

$y=3x-5$

$y=3\times0-5$

$y=0-5$

$y=-5$

The point that the line crosses the y-axis is at point $(0,-5)$ which means that the answer is neither a, b, c, or d.