Question

11 in slope - intercept form, write the equation of the graphed line.

12 in slope - intercept form, write the equation of the line if the pitch is \\(\frac{2}{7}\\) goes through the point \\((14, - 5)\\)

13 in slope - intercept form, write the equation of the line if the rise is 5, the run is 3 and \\(b = 4\\)

Explanation:

Question 11

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, -1)\) (the y - intercept) and another point, say \((5, 2)\) (by counting the grid).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((x_1,y_1)=(0, - 1)\) and \((x_2,y_2)=(5,2)\), we have \(m=\frac{2-(-1)}{5 - 0}=\frac{3}{5}\)? Wait, no, let's re - check. Wait, looking at the graph again, when \(x = 0\), \(y=-1\) (y - intercept \(b=-1\)), and when \(x = 5\), \(y = 2\)? Wait, maybe a better pair: from \((-5,-4)\) to \((0,-1)\). Then \(m=\frac{-1-(-4)}{0 - (-5)}=\frac{3}{5}\)? Wait, no, the line passes through \((-5,-4)\) and \((0,-1)\) and \((5,2)\). So the slope \(m=\frac{-1-(-4)}{0 - (-5)}=\frac{3}{5}\)? Wait, no, let's calculate the slope between \((-5,-4)\) and \((0,-1)\): \(m=\frac{-1 - (-4)}{0-(-5)}=\frac{3}{5}\). And the y - intercept \(b=-1\) (since when \(x = 0\), \(y=-1\)). So the slope - intercept form is \(y=mx + b\), so \(y=\frac{3}{5}x-1\)? Wait, but maybe I made a mistake. Wait, let's check another pair. From \((-5,-4)\) to \((5,2)\): the change in \(y\) is \(2-(-4)=6\), change in \(x\) is \(5-(-5)=10\), so \(m=\frac{6}{10}=\frac{3}{5}\). And the y - intercept is at \((0,-1)\). So the equation is \(y=\frac{3}{5}x-1\).

Step1: Recall slope - intercept form

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know that \(m=\frac{2}{7}\) and the line passes through the point \((x_1,y_1)=(14,-5)\).

Step2: Substitute into the equation to find \(b\)

Substitute \(x = 14\), \(y=-5\) and \(m=\frac{2}{7}\) into \(y=mx + b\): \(-5=\frac{2}{7}\times14 + b\).
First, calculate \(\frac{2}{7}\times14\): \(\frac{2}{7}\times14 = 4\). So the equation becomes \(-5 = 4 + b\).

Step3: Solve for \(b\)

Subtract 4 from both sides: \(b=-5 - 4=-9\).

Step4: Write the equation

Now that we have \(m=\frac{2}{7}\) and \(b = - 9\), the slope - intercept form is \(y=\frac{2}{7}x-9\).

Step1: Calculate the slope \(m\)

The slope \(m\) is defined as \(\frac{\text{rise}}{\text{run}}\). Given that the rise is 5 and the run is 3, so \(m=\frac{5}{3}\).

Step2: Recall slope - intercept form

The slope - intercept form of a line is \(y = mx + b\). We know that \(m=\frac{5}{3}\) and \(b = 4\).

Step3: Write the equation

Substitute \(m=\frac{5}{3}\) and \(b = 4\) into \(y=mx + b\), we get \(y=\frac{5}{3}x+4\).

Answer:

\(y = \frac{3}{5}x-1\)

Question 12