Graph the following equation: clculte the slope, x-intercept, and y-intercept, and label the the intercelts on the graph.
problem: Find an equationin slope-intercept form passing through the points (2,5) and ( 7,-3).
To find the equation in slope-intercept form passing through the given points (2,5) and (7,-3), we first need to calculate the slope. The formula to find the slope between two points (x1,y1) and (x2,y2) is given by:
slope (m) = (y2 - y1) / (x2 - x1)
Using the coordinates (2,5) and (7,-3):
slope (m) = (-3 - 5) / (7 - 2)
= -8 / 5
The slope of the line passing through these two points is -8/5.
Next, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is given by:
y - y1 = m(x - x1)
Using the point (2,5) and the slope -8/5:
y - 5 = -8/5(x - 2)
Now, we can convert this equation into slope-intercept form (y = mx + b), where b represents the y-intercept. We simplify the equation further:
y - 5 = -8/5x + 16/5
y = -8/5x + 16/5 + 25/5
y = -8/5x + 41/5
Now that we have the equation in slope-intercept form, let's plot the graph and find the x-intercept and y-intercept.
Graph:
To plot the graph, we need to choose a suitable range for the x-axis and y-axis, based on the given points and the equation.
Let's choose the x-axis range from -2 to 10, and the y-axis range from -10 to 10.
Plot the points (2,5) and (7,-3) on the graph, and draw a line passing through these two points using the equation y = -8/5x + 41/5.
The x-intercept is the value of x when y = 0. To find the x-intercept, we set y = 0 in the equation and solve for x:
0 = -8/5x + 41/5
8/5x = 41/5
x = (41/5) / (8/5)
x = 41/8
So, the x-intercept is (41/8, 0).
The y-intercept is the value of y when x = 0. To find the y-intercept, we set x = 0 in the equation and solve for y:
y = -8/5(0) + 41/5
y = 41/5
So, the y-intercept is (0, 41/5).
Label these points on the graph, and you have successfully graphed the equation, found the slope, and identified the x-intercept and y-intercept.