A linear function is used to represent the equation of a straight line.
Given
[tex]y = -\frac 34x + 2[/tex] --- Aisha
[tex]y = \frac{3}{-4}x + 2[/tex] --- Carolina
(a) How they use different step
A linear equation is represented as:
[tex]y = mx + b[/tex]
Where:
[tex]m \to[/tex] slope
[tex]b \to[/tex] y intercept
and
[tex]m = \frac{rise}{run}[/tex]
For Aisha's graph;
[tex]m = \frac{-3}{4}[/tex]
By comparison:
[tex]rise = -3[/tex]
[tex]run = 4[/tex]
This means that Aisha's graph has a rise of -3 and a run of 4
i.e. the other point used to calculate the slope is gotten by moving 3 units down and 4 units left of the y-intercept.
For Carolina's graph;
[tex]n = \frac{3}{-4}[/tex]
By comparison:
[tex]rise = 3[/tex]
[tex]run = -4[/tex]
This means that Carolina's graph has a rise of 3 and a run of -4
i.e. the other point used to calculate the slope is gotten by moving 3 units up and 4 units right of the y-intercept.
(b) Will the graph look the same?
Recall that:
[tex]y = mx + b[/tex]
[tex]m \to[/tex] slope
[tex]b \to[/tex] y intercept
For Aisha's graph
[tex]y = -\frac 34x + 2[/tex]
The slope is:
[tex]m = -\frac{3}{4}[/tex]
[tex]m = -0.75[/tex]
The y intercept is:
[tex]b = 2[/tex]
For Carolina's graph
[tex]y = \frac{3}{-4}x + 2[/tex]
The slope is:
[tex]m = \frac{3}{-4}[/tex]
[tex]m = -0.75[/tex]
The y intercept is:
[tex]b = 2[/tex]
Both equations have the same slope and the same y-intercept.
Hence, the graphs will look the same
See attachment for the graphs of their equations.
Read more about linear functions at:
https://brainly.com/question/20286983
