HELP.
Problems 4 - 7: Write an equation for the line in point/slope form and slope/intercept form that has the given condition.
4. Slope = 3/2 and passes through the origin.
5. x-intercept = 4 and y-intercept = -3
#4:
(y-0)/(x-0) = 3/2
y = 3/2 x
#5: 3x-4y=12
(y-0)/(x-4) = (-3-0)/(0-4)
or, y/(x-4) = 3/4
y = 3/4 x - 3
the square of the larger of two consecutive integers is 34 less than twice the square of the smaller consecutive integer.
No problem, I'll help you with both problems.
Problem 4:
To write the equation of a line in point/slope form, we need a point on the line and the slope of the line. In this case, we're given the slope of the line, which is 3/2, and it passes through the origin, which is the point (0, 0).
Point/slope form: y - y1 = m(x - x1)
Substituting the given values, we have:
y - 0 = (3/2)(x - 0)
Simplifying, we get:
y = (3/2)x
So the equation of the line in point/slope form is y = (3/2)x.
To convert this equation to slope/intercept form, where the equation is in the form y = mx + b (m is the slope, and b is the y-intercept), we can see that in this case, the y-intercept is 0, as it passes through the origin.
Slope/intercept form: y = mx + b
Substituting the given slope and the y-intercept, we have:
y = (3/2)x + 0
Simplifying, we get:
y = (3/2)x
So the equation of the line in slope/intercept form is y = (3/2)x.
Problem 5:
To write the equation of a line when we're given the x-intercept and the y-intercept, we need to use the intercepts to find two points on the line, and then use one of the methods (like point/slope form or two-point form) to find the equation.
Given x-intercept = 4, and y-intercept = -3, we can see that the corresponding points are (4, 0) and (0, -3).
Using point/slope form, we can choose any of the two points and the provided slope (which in this case will be 0 since the line is horizontal).
Point/slope form: y - y1 = m(x - x1)
Using the point (4, 0), and substituting the given values:
y - 0 = 0(x - 4)
Simplifying, we get:
y = 0
So the equation of the line in point/slope form is y = 0.
To convert this equation to slope/intercept form, we see that the y-intercept is -3.
Slope/intercept form: y = mx + b
Substituting the given slope and the y-intercept, we have:
y = 0x - 3
Simplifying, we get:
y = -3
So the equation of the line in slope/intercept form is y = -3.
I hope this helps! Let me know if you have any further questions.