A line passes through the point $$ (-2,1) $$ and has a slope of $$ \frac{5}{2} $$. Write an equation in slope-intercept form for this line.

Question

UpStudy AI · Accepted Answer

To find the equation of a line in slope-intercept form, we use the formula:

$$
y = mx + b
$$

where $$ m $$ is the slope and $$ b $$ is the y-intercept.

Given:
- The slope $$ m = \frac{5}{2} $$
- The point $$ (-2, 1) $$

We can substitute the slope and the coordinates of the point into the equation to find $$ b $$.

1. Substitute $$ x = -2 $$, $$ y = 1 $$, and $$ m = \frac{5}{2} $$ into the equation:

$$
1 = \frac{5}{2}(-2) + b
$$

2. Calculate $$ \frac{5}{2}(-2) $$:

$$
\frac{5}{2}(-2) = -5
$$

3. Substitute this value back into the equation:

$$
1 = -5 + b
$$

4. Solve for $$ b $$:

$$
b = 1 + 5 = 6
$$

Now we have both $$ m $$ and $$ b $$:

- Slope $$ m = \frac{5}{2} $$
- Y-intercept $$ b = 6 $$

Thus, the equation of the line in slope-intercept form is:

$$
y = \frac{5}{2}x + 6
$$
The equation of the line in slope-intercept form is $$ y = \frac{5}{2}x + 6 $$.

A line passes through the point \( (-2,1) \) and has a slope of \( \frac{5}{2} \). Write an equation in slope-intercept form for this line.