x y

Question

11 | 58
20|103 Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y=mx+b form.

Answer 1

To find the equation of the linear function that models the relationship between x and y given the points (11, 58) and (20, 103), we first need to determine the slope (m) of the line. The slope is calculated using the formula:

$$m=\frac{y_2-y_1}{x_2-x_1}$$

Here, we can assign:

• $(x_1,y_1)=(11,58)$
• $(x_2,y_2)=(20,103)$

Now, substituting the values into the slope formula:

$$m=\frac{103-58}{20-11}=\frac{45}{9}=5$$

Now that we have the slope $m=5$, we can use the point-slope form of a linear equation to find the y-intercept (b). We can use either of the two points; let's use the point (11, 58):

The point-slope form is:

$$y-y_1=m(x-x_1)$$

Substituting the values into this equation:

$$y-58=5(x-11)$$

Now we solve for $y$:

$$y-58=5x-55$$ $$y=5x-55+58$$ $$y=5x+3$$

Thus, the equation of the linear function in $y=mx+b$ form is:

$$\boxed{{\displaystyle y=5x+3}}$$

Answer 2

Write the equation of the linear function shown on the graph. Enter your answer in y=mx+b form. (1 point) (2,4) (-3,-1)

Answer 3

To determine the equation of the linear function that passes through the points $(2,4)$ and $(-3,-1)$, we need to find the slope (m) and then use one of the points to find the y-intercept (b).

1. Calculate the slope (m) using the formula:

$$m=\frac{y_2-y_1}{x_2-x_1}$$

Here, we can assign:

• $(x_1,y_1)=(2,4)$
• $(x_2,y_2)=(-3,-1)$

Substituting these values into the slope formula:

$$m=\frac{-1-4}{-3-2}=\frac{-5}{-5}=1$$

2. Now that we have the slope $m=1$, we can use the point-slope form to find the equation of the line. Using point $(2,4)$:

The point-slope form is:

$$y-y_1=m(x-x_1)$$

Substituting the known values:

$$y-4=1(x-2)$$

Now, we can simplify and solve for $y$:

$$y-4=x-2$$ $$y=x-2+4$$ $$y=x+2$$

Thus, the equation of the linear function in $y=mx+b$ form is:

$$\boxed{{\displaystyle y=x+2}}$$