Find the linear function whose graph passes through the point ...

Question

Find the linear function whose graph passes through the point (3, 2) and is parallel to the line $y = 3 x + 8$ .

Accepted Answer

Welcome back everyone. In this problem, a function is defined as a straight line passing through the point 13. This function is parallel with the line described by the equation y equals 2x plus 5 And we want to figure out the equation of our function. For our answer choices, a is y equals 2x plus 2. B is y equals 2x plus 1. C is y equal to x and the d is y equals 2x minus 1. Now, most times I find it helpful to try and visualize what we're thinking about here. So basically, what we're saying is that we have a line. Okay. That's described by the equation y equals 2x+5. So probably our line looks something like this. And we have a function that we don't know yet, but we know that it is parallel to our line described, y equal to x plus 5. So that means if I were to draw it, then it would probably be something that looks like this. And we also know that it passes through the point 13. That's all we know about our function. And we want to figure out what the equation of that function is. Now recall that for any linear function, it's written in the form y equals mx plus c, where m is our gradient and c is our y intercept. Now, notice the gradient or the slope. Let me add the word slope because some of us might be more familiar with the word slope. Now, also, recall that when two lines are parallel so when two lines are parallel Okay. Their slopes are equal. So what does that tell us then? Already, that tells us that for our function so the for the equation of our function, its its slope would also be equal to 2. Now that we have its slope, all we need is its y intercept. In order to find its y intercept, what can help us? Well, we know that it passes through the point 13. So, so far, we already know that our line y equals 2x+c. We don't know what c is yet. But since it passes through 13, we have x and y coordinates that we can use to help us figure out the value of its y intercept to c. So, substituting 1 3 to find the y intercept of our function. Okay. Then that means our function is now going to become y equals. Well, what do we know? We know our coordinate is written in the form x y. So y is actually 3. So 3 equals 2 multiplied by 1 plus c. Now we can go ahead and solve for y intercept. 2 multiplied by 1 is 2 and that means c would be equal to 3 minus 2 which equals 1. Know that we have our y intercept 1 and we have our gradient 2. That means the equation of our function. The equation of our function is y equals 2x2 for the slope plus 1, 1 for the y intercept. And when we look on our answer choices, that would be answer choice b. Thanks a lot for watching everyone. I hope this video helped.

Find the linear function whose graph passes through the point (3, 2) and is parallel to the line $y = 3 x + 8$ .

Key Concepts

Linear Functions

Slope

Point-Slope Form

Watch next

Find the linear function whose graph passes through the point (3, 2) and is parallel to the line y=3x+8y= 3x + 8 .

Key Concepts

Linear Functions

Slope

Point-Slope Form

Watch next

Find the linear function whose graph passes through the point (3, 2) and is parallel to the line $y = 3 x + 8$ .