Which is the equation of a line that has a slope of One-half and passes through point (2, –3)?

Question

y = one-half x minus 4
y = one-half x minus 2
y = one-half x + 2
y = one-half x + 3

Answer 1

To find the equation of a line with a given slope and a point, you can use the point-slope form of the equation of a line:

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

where $m$ is the slope and $(x_1,y_1)$ is the point on the line.

Given:

• Slope ($m$) = $\frac{1}{2}$
• Point ($x_1,y_1$) = $(2,-3)$

Plugging these values into the formula:

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

This simplifies to:

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

Now, distribute the slope on the right side:

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

Next, isolate $y$ by subtracting 3 from both sides:

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

So the equation of the line is:

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

Therefore, the correct option is: y = one-half x minus 4.