Question

The graph of a line on a coordinate plane has a slope of 1/2 and passes through the point (4, -3). Which equation describes the line?

Answer 1

Answer:

$\boxed {\boxed {\sf y= \frac{1}{2}x-5 }}$

Step-by-step explanation:

Since we are given a point and a slope, we should use the point-slope equation.

$y-y_1=m(x-x_1)$

where m is the slope and (x₁, y₁) is the point the line passes through.

We are given the slope of 1/2 and the point (4, -3). Therefore:

$m= \frac{1}{2} \\x_1= 4\\y_1= -3$

Substitute the values into the formula.

$y--3= \frac{1}{2} (x-4)$

$y+ 3= \frac{1}{2} (x-4)$

Distribute the 1/2. Multiply each term inside the parentheses by 1/2.

$y+3= \frac{1}{2} *x + \frac{1}{2} * -4$

$y+3=\frac{1}{2}x-2$

We want to the equation of the line in slope-intercept form or y=mx+b. We need to isolate y. 3 is being added and the inverse of addition is subtraction. Subtract 3 from both sides of the equation.

$y+3-3=\frac{1}{2}x-2-3$

$y=\frac{1}{2}x-2-3\\y= \frac{1}{2}x-5$

The equation of the line is y=1/2x-5