Find the equation of a straight line through two given points

What is the equation of the line passing through A and B?

What is the equation of the line passing through (2, 5) and (4, 11)?

What is the equation of the line passing through (4, -5) and (2, 1)?

Which of these coordinates is on the line which passes through (3, -7) and (-1, 1)?

﻿Hello, my name is Miss Parnham. In this lesson we're going to learn how to interpret gradient and intercept on real life graphs. Here we have a graph showing the mass of a container in kilogrammes when it is filled with boxes. And each box has the same mass. So let's look at the Y intercept of the graph. We can see that it intercepts at positive two. And what does that represent? Well that means when there are zero boxes so when x is zero, y is two. So it must be the mass of the container itself. And what's the gradient of the graph? So we can pick any two coordinates that are easy to read, let's try 1,3 and 2,4. We can see the vertical change is one and the horizontal change is one. So that means the gradient is one divided by one or one. And this means that every time we ad a box we add one kilogramme, so it represents the mass of each box. So the empty container has a mass of two kilogrammes and each box has a mass of one kilogramme. Here's a question for you to try. Pause the video to complete the task and then restart the video when you're finished. Here are the answers, on this conversion graph you could use any two pairs of coordinates to find the gradient. It's probably easiest if one of them is 0,0. So if we use say 0,0 and 5,4 then the vertical change divided by the horizontal change is four over five and you can leave that as 4/5 or call it 0.8 either is acceptable. And what does that actually represent? Well we've divided the price by the kilogrammes so it is priced per kilogrammes. Here's another question for you to try. Pause the video to complete the task and then restart the video when you're finished. Here are the answers, when we work out the gradient we use two coordinates which are easy to read. So for this graph we have 0,2 and 8,10. The vertical change and the horizontal change you can see from those two coordinates are both eight. So that gives us a gradient of one. Eight divided by eight is one. And we can see that this graph intercepts at two. So regardless of the distance you go in the taxis there is standard charge of two pounds. And then when we found the gradient by dividing the price by the distance. So the gradient is the price per mile. That's all for this lesson thank you for watching.

Interpret gradient and intercept on real life graphs

What is the equation of the line in this conversion graph?

What does the gradient represent on this conversion graph?

The graph shows the cost of one person going ten-pin bowling, including the standing charge for shoe hire. How much does it cost to hire bowling shoes?

The graph shows the cost of one person going ten-pin bowling, including the standing charge for shoe hire. How much does each game cost each person?

In this lesson, we will calculate and interpret the gradient and intercepts on real life graphs. We will draw upon our skills of drawing triangles to calculate gradients.

Maths

Y11 Maths (Core)

Key Stage 4

Year 11

Miss

Y11 Maths (Foundation)

Y10 Maths (Higher)

Year 10

Y10 Maths (Core)

Straight Line Graphs 2 (Parallel Lines)

Algebra (A)

THEME

UNIT

Write the equation of a straight line if parallel to a line and passing through (0,n)

Write the equation of a straight line if parallel to a line and passing through any point

1. Which of these lines is parallel to y = −2𝑥 + 5?

2. Which of these lines is parallel to y = −2𝑥 + 5 and passes through (3, 2)?

1. Which of these lines is parallel to y = 3𝑥 + 4?

2. Which of these lines is parallel to y = 3𝑥 + 4 and passes through (0, 8)?

Lesson overview:Interpret gradient and intercept on real life graphs

Core Content

Straight Line Graphs 2 (Parallel Lines):