Question

there is a coordinate grid with a line segment. the x - axis and y - axis are labeled from 0 to 10. one endpoint of the line is at (0, 4) and the other at (7, 8) (assuming the grid lines are 1 unit each, but the exact problem description is missing as the question part is not fully visible).

Explanation:

To determine the equation of the line, we first identify two points on the line. From the graph, we can see that the line passes through \((0, 4)\) and \((7, 8)\) (assuming the coordinates are \((x, y)\) with \(x\) along the horizontal axis and \(y\) along the vertical axis, and the grid lines represent integer values).

Step 1: Calculate the slope (\(m\))

The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting \((x_1, y_1) = (0, 4)\) and \((x_2, y_2) = (7, 8)\):
\[
m = \frac{8 - 4}{7 - 0} = \frac{4}{7}
\]

Step 2: Determine the y-intercept (\(b\))

The y-intercept is the value of \(y\) when \(x = 0\). From the point \((0, 4)\), we can see that when \(x = 0\), \(y = 4\). So, \(b = 4\).

Step 3: Write the equation of the line

The slope-intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Substituting \(m = \frac{4}{7}\) and \(b = 4\), we get:
\[
y = \frac{4}{7}x + 4
\]

If we want to find other properties, such as the x-intercept (where \(y = 0\)):

Step 4: Find the x-intercept

Set \(y = 0\) in the equation \(y = \frac{4}{7}x + 4\) and solve for \(x\):
\[
0 = \frac{4}{7}x + 4
\]
Subtract 4 from both sides:
\[
-4 = \frac{4}{7}x
\]
Multiply both sides by \(\frac{7}{4}\):
\[
x = -4 \times \frac{7}{4} = -7
\]
So the x-intercept is at \((-7, 0)\).

If the question was about finding the equation, slope, intercepts, or other properties of the line, the above steps apply. For example, if the question was "Find the equation of the line in slope-intercept form," the answer would be \(y = \frac{4}{7}x + 4\).

Answer:

To determine the equation of the line, we first identify two points on the line. From the graph, we can see that the line passes through \((0, 4)\) and \((7, 8)\) (assuming the coordinates are \((x, y)\) with \(x\) along the horizontal axis and \(y\) along the vertical axis, and the grid lines represent integer values).

Step 1: Calculate the slope (\(m\))

The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting \((x_1, y_1) = (0, 4)\) and \((x_2, y_2) = (7, 8)\):
\[
m = \frac{8 - 4}{7 - 0} = \frac{4}{7}
\]

Step 2: Determine the y-intercept (\(b\))

The y-intercept is the value of \(y\) when \(x = 0\). From the point \((0, 4)\), we can see that when \(x = 0\), \(y = 4\). So, \(b = 4\).

Step 3: Write the equation of the line

The slope-intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Substituting \(m = \frac{4}{7}\) and \(b = 4\), we get:
\[
y = \frac{4}{7}x + 4
\]

If we want to find other properties, such as the x-intercept (where \(y = 0\)):

Step 4: Find the x-intercept

Set \(y = 0\) in the equation \(y = \frac{4}{7}x + 4\) and solve for \(x\):
\[
0 = \frac{4}{7}x + 4
\]
Subtract 4 from both sides:
\[
-4 = \frac{4}{7}x
\]
Multiply both sides by \(\frac{7}{4}\):
\[
x = -4 \times \frac{7}{4} = -7
\]
So the x-intercept is at \((-7, 0)\).

If the question was about finding the equation, slope, intercepts, or other properties of the line, the above steps apply. For example, if the question was "Find the equation of the line in slope-intercept form," the answer would be \(y = \frac{4}{7}x + 4\).