The linear function equation is [tex]\boxed{y = \frac{1}{3}x - 4}.[/tex]
Further explanation:
The formula for slope of line can be expressed as,
[tex]\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]
Explanation:
The line intersect [tex]\text{y}[/tex]-axis at [tex]\left( {0,- 4} \right).[/tex]
Therefore, the [tex]\text{y}[/tex]-intercept is -4.
The line passes through the points [tex]\left( {0,- 4} \right)[/tex] and [tex]\left( {3,- 3} \right)[/tex].
The slope can be obtained as follows,
[tex]\begin{aligned}m &= \frac{{- 3 - \left( { - 4} \right)}}{{3 - 0}}\\&= \frac{{ - 3 + 4}}{3}\\&= \frac{1}{3}\\\end{aligned}[/tex]
The slope of the line is [tex]\dfrac{1}{3}.[/tex]
The slope intercept form of the linear equation is given as follows.
[tex]\boxed{y = mx + k}[/tex]
Substitute [tex]\dfrac{1}{3}[/tex] for m and -4 for k in equation [tex]y = mx + k.[/tex]
[tex]y = \dfrac{1}{3}x - 4[/tex]
The linear function equation is [tex]\boxed{y = \frac{1}{3}x - 4}.[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: graph function, numbers, slope, slope intercept, equation, linear function, linear equation, y-intercept, graph, representation, origin.
