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$A line with a slope of 2 passes through the point (4,10). What is its equation in slope-intercept form? Write your answer using integers, proper fractions, and improper fractions in simplest form. Submit$

A line with a slope of $2$ passes through the point $(4,10)$ . What is its equation in slope-intercept form? $\newline$ Write your answer using integers, proper fractions, and improper fractions in simplest form. $\newline$ Submit

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Math Problems

Grade 8

Write a linear equation from a slope and a point

Full solution

Q. A line with a slope of

2

passes through the point

(4,10)

. What is its equation in slope-intercept form?

\newline

Write your answer using integers, proper fractions, and improper fractions in simplest form.

\newline

Submit

Identify Linear Equation Form: Identify the slope-intercept form of a linear equation. $\newline$ The slope-intercept form of a linear equation is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
Find Y-Intercept: Use the given slope and point to find the y-intercept $b$ . We know the slope $m$ is $2$ and the line passes through the point $(4,10)$ . We can use the point-slope form to find $b$ : $y - y_1 = m(x - x_1)$ $10 - y_1 = 2(4 - x_1)$ Since the point $(4,10)$ is on the line, we substitute $x_1$ with $4$ and $y_1$ with $10$ : $10 - 10 = 2(4 - 4)$ $0 = 2(0)$ $0 = 0$ This doesn't give us $b$ directly, so we need to use the slope-intercept form and solve for $b$ using the point $(4,10)$ .
Substitute and Solve for B: Substitute the slope and coordinates of the point into the slope-intercept form to solve for $b$ . $y = mx + b$ $10 = 2(4) + b$ $10 = 8 + b$ Subtract $8$ from both sides to solve for $b$ : $10 - 8 = b$ $2 = b$
Write Equation in Form: Write the equation of the line in slope-intercept form using the slope and y-intercept. $\newline$ Now that we have the slope $m = 2$ and the y-intercept $b = 2$ , we can write the equation: $\newline$ $y = mx + b$ $\newline$ $y = 2x + 2$