Question

Which equation of a line passes through the point $(-2,3)$ and has slope of $\frac{3}{4}$?

• A. $y-3=\frac{3}{4}(x+2)$
• B. $y+3=\frac{3}{4}(x-2)$
• C. $y+2=\frac{3}{4}(x-3)$

Answer 1

The correct option is A

$y-3=\frac{3}{4}(x+2)$

Explanation for the correct option:

Option A: $y-3=\frac{3}{4}(x+2)$, lets check $(-2,3)$ satisfies the equation or not.

Substitute $x=-2,y=3$;

$$\begin{gathered} \Rightarrow 3-3=\frac{3}{4}(-2+2) \\ \Rightarrow 0=0 \end{gathered}$$

Therefore, $(-2,3)$ satisfies the equation.

Clearly, $\frac{3}{4}$is slope of equation. (when we compare given function with $y=mx+c$ coefficient of x is slope, here coefficient of x is $\frac{3}{4}$.)

Explanation for the incorrect options:

Option B: $y+3=\frac{3}{4}(x-2)$, lets check $(-2,3)$ satisfies the equation or not.

Substitute $x=-2,y=3$;

$$\begin{gathered} \Rightarrow 3+3=\frac{3}{4}(-2-2) \\ \Rightarrow 6=\frac{3}{4}(-4) \\ \Rightarrow 6\ne -3 \end{gathered}$$

Not satisfied.

Option C: $y+2=\frac{3}{4}(x-3)$, lets check $(-2,3)$ satisfies the equation or not.

Substitute $x=-2,y=3$;

$$\begin{gathered} \Rightarrow 3+2=\frac{3}{4}(-2-3) \\ \Rightarrow 5=\frac{3}{4}(-5) \\ \Rightarrow 5\ne \frac{-15}{4} \end{gathered}$$

Not satisfied.

Thus, option A is correct.