Explanation:
We can set up an equation for this line using slope intercept form:
![y = mx + b](https://img.qammunity.org/2022/formulas/mathematics/high-school/hi7nib56czgdtaz3ud2tuzvr49eqo8cnyj.png)
Where
is the slope of the line and
is the y-intercept (where the line cross the Y-axis at
).
We know that the slope of the line is
so we can plug that in for
, but we don't know
, so we'll have to use the given point
to help solve for it:
![y = -4x + b](https://img.qammunity.org/2022/formulas/mathematics/high-school/keu21omc8jcclg499pb7jc88e85mfpacg5.png)
![-10 = -4(-6) + b](https://img.qammunity.org/2022/formulas/mathematics/high-school/oyzjeu3c9u75dm5o2zcsshrh1wj028sbs0.png)
![-10 = 24 + b](https://img.qammunity.org/2022/formulas/mathematics/high-school/mvfdu9fdync4y1kye4leu89c7vmqmx6y4a.png)
![b = -34](https://img.qammunity.org/2022/formulas/mathematics/high-school/ws2grzhofrlqgmja6rqiwbcckn3lcjesa9.png)
This means the equation of the line is
. Now we can plug in the point
and solve for
:
![y = -4x - 34](https://img.qammunity.org/2022/formulas/mathematics/high-school/sk2tpquiykp2ivck3r37gj9kfnd4fub7u9.png)
![s = -4(-9) - 34](https://img.qammunity.org/2022/formulas/mathematics/high-school/chhu3q7ah4nfhdqttxytrtdzwjr69csu1j.png)
![s = 36 - 34](https://img.qammunity.org/2022/formulas/mathematics/high-school/b04haw2akkn0xf3hz0jin4ekjv6zfv7wl1.png)
![s = 2](https://img.qammunity.org/2022/formulas/geography/high-school/xwu71whu3v4urr96xhe01es7b5pymf536m.png)