Answer:
[tex]f(x)=\frac{2}{3}x+3[/tex]
Step-by-step explanation:
Let
[tex]A(-3,1), B(0,3)[/tex]
Find the slope AB
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{3-1}{0+3}[/tex]
[tex]m=\frac{2}{3}[/tex]
we know that
The equation of the line into slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-coordinate of the y-intercept
In this problem we have
[tex]m=\frac{2}{3}[/tex]
[tex]b=3[/tex] -----> the y-coordinate of point B
substitute
[tex]f(x)=\frac{2}{3}x+3[/tex]
The linear function is [tex]\boxed{\frac{2}{3}x + 3}[/tex] that represents the given graph.
Further explanation:
Explanation:
The line intersect [tex]\text{y}[/tex]-axis at [tex]\left( {0,3} \right).[/tex]
Therefore, the [tex]\text{y}[/tex]-intercept is 3.
The formula for slope of line with points [tex]\left( {{x_1},{y_1}} \right)[/tex] and [tex]\left( {{x_2},{y_2}} \right)[/tex] can be expressed as,
[tex]\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]
The line the line passes through the points [tex]\left( {0,3} \right)[/tex] and [tex]\left( {-3,1} \right).[/tex]
The slope can be obtained as follows,
[tex]\begin{aligned}m&= \frac{{1 - 3}}{{ - 3 - 0}}\\&= \frac{{ - 2}}{{ - 3}}\\&= \frac{2}{3}\\\end{aligned}[/tex]
The slope of the line is [tex]\dfrac{2}{3}.[/tex]
The linear equation with slope m and intercept c is given as follows.
[tex]\boxed{y = mx + c}[/tex]
Substitute [tex]\dfrac{2}{3}[/tex] for m and 3 for c in equation [tex]y = mx + c.[/tex]
[tex]y = \dfrac{2}{3}x + 3[/tex]
The linear function is [tex]\boxed{\frac{2}{3}x + 3}[/tex] that represents the given graph.
Learn more:
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: graph function, numbers, slope, slope intercept, equation, linear equation, linear function, y-intercept, graph, representation, origin.
