Find the equation of the line with a slope of $$ m=8 $$ that passes through the point $$ (4,2) $$. Write the equation in both the point-slope form and the slope-intercept form. point-slope: slope-intercept:

Question

UpStudy AI · Accepted Answer

**Step 1. Write the point-slope form**

The point-slope form of a line is given by:
$$
y - y_1 = m(x - x_1)
$$
where $$ m $$ is the slope and $$(x_1, y_1)$$ is a point on the line.

Given $$ m = 8 $$ and the point $$(4,2)$$, substitute these values into the formula:
$$
y - 2 = 8(x - 4)
$$

**Step 2. Convert to the slope-intercept form**

The slope-intercept form of a line is:
$$
y = mx + b
$$

Starting with the point-slope form:
$$
y - 2 = 8(x - 4)
$$
Distribute $$8$$ on the right-hand side:
$$
y - 2 = 8x - 32
$$
Now, add $$2$$ to both sides to solve for $$y$$:
$$
y = 8x - 32 + 2
$$
$$
y = 8x - 30
$$

**Answer:**

point-slope:
$$
y - 2 = 8(x - 4)
$$

slope-intercept:
$$
y = 8x - 30
$$
point-slope: $$ y - 2 = 8(x - 4) $$ slope-intercept: $$ y = 8x - 30 $$

Find the equation of the line with a slope of \( m=8 \) that passes through the point \( (4,2) \). Write the equation in both the point-slope form and the slope-intercept form. point-slope: slope-intercept:

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Algebra Questions