Question

# State the gradient and y-intercept of the line y = -3x + 8.

Hint:

### Gradient is also called the slope of the line. The slope intercept form of the equation of the line is y = mx + c, where m is the slope of the line and c is the y-intercept. The given equation is already in this form. We compare the given equation with this form to get the slope and the y-intercept.

## The correct answer is: we get Gradient = -3 y-intercept = 8

### Step by step solution:

The given equation of the line is

y = - 3x + 8

Comparing the above equation with

y = mx + c

We get

m = -3; c = 8

Thus, we get

Gradient = -3

y-intercept = 8

Comparing the above equation with

We get

Thus, we get

The student needs to remember all the different forms of equation of a line and what each term and notation signifies in the equation.

We can find the slope and y-intercept directly from the general form of the equation too; slope = and y-intercept =, where the general form of equation of a line is ax + by + c = 0.

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¶The standard form of a linear equation in one variable is: ax + b = 0

Where,

The letters 'a' and 'b' are real numbers.

'a' and 'b' are both greater than zero.

### In an academic contest correct answers earn 12 points and incorrect answers lose 5

points. In the final round, school A starts with 165 points and gives the same number

of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.

ii)How many answers did each school get correct in the final round?

A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. 2x+3=8, for example, is a linear equation with a single variable. As a result, this equation has only one solution, x = 5/2.

¶The standard form of a linear equation in one variable is: ax + b = 0

Where,

The letters 'a' and 'b' are real numbers.

'a' and 'b' are both greater than zero.