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2

ABC

g(x) is a linear function with a slope of 3 and
g(10)=26. What is the value of
g(6) ?

$2$ $\newline$ $A B C$ $\newline$ $g(x)$ is a linear function with a slope of $3$ and $g(10)=26$ . What is the value of $g(6)$ ?

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Write a linear equation from a slope and y-intercept

Full solution

Q.

2

\newline

A B C

\newline

g(x)

is a linear function with a slope of

3

and

g(10)=26

. What is the value of

g(6)

?

Identify Linear Equation Form: Identify the slope-intercept form of a linear equation. The general form is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
Find y-Intercept: Use the given point $(10, 26)$ to find $b$ . $\newline$ Substitute $m = 3$ and $x = 10$ , $y = 26$ into the equation: $\newline$ $26 = 3(10) + b$ $\newline$ $26 = 30 + b$ $\newline$ $b = 26 - 30$ $\newline$ $b = -4$
Write Equation of $g(x)$ : Write the equation of $g(x)$ using the slope and y-intercept. $\newline$ $g(x) = 3x - 4$
Calculate $g(6)$ : Calculate $g(6)$ using the equation. $\newline$ Substitute $x = 6$ into $g(x) = 3x - 4$ : $\newline$ $g(6) = 3(6) - 4$ $\newline$ $g(6) = 18 - 4$ $\newline$ $g(6) = 14$

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