Question

# Sketch the graph of y = 2x - 5.

Hint:

### A linear equation is in the form ax + by + c=0. A graph is a geometrical representation of an equation. A coordinate point (x, y) consists of the distance from the horizontal and vertical axis as coordinates.

We are asked to sketch the graph of the given equation.

## The correct answer is: - 3

### Step 1 of 2:

Find two coordinate points of the equation.

When x = 0,

y = 2x - 5

y = 2(0) - 5

y = 0 - 5

y = - 5

When x = 1,

y = 2x - 5

y = 2(1) - 5

y = 2 - 5

y = - 3

Thus, the required points are: .

Step 2 of 2:

Plot the points and join them to get the graph of the equation.

Thus, the graph is:

We only require just two coordinate points to graph a linear equation in two variables. In case of a quadratic equation we would need at least three coordinate points.

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### Write the equation in slope-intercept form of the line that passes through the points (5, 4) and (-1, 6).

The slope intercept form is y = mx + b, where m represents the slope and b represents the y-intercept. We can draw the graph of a linear equation on the x-y coordinate plane using this form of a linear equation.

Steps for determining a line's equation from two points:

Step 1: The slope formula used to calculate the slope.

Step 2: To determine the y-intercept, use the slope and one of the points (b).

Step 3: Once you know the values for m and b, we can plug them into the slope-intercept form of a line, i.e., (y = mx + b), to obtain the line's equation.

### Write the equation in slope-intercept form of the line that passes through the points (5, 4) and (-1, 6).

The slope intercept form is y = mx + b, where m represents the slope and b represents the y-intercept. We can draw the graph of a linear equation on the x-y coordinate plane using this form of a linear equation.

Steps for determining a line's equation from two points:

Step 1: The slope formula used to calculate the slope.

Step 2: To determine the y-intercept, use the slope and one of the points (b).

Step 3: Once you know the values for m and b, we can plug them into the slope-intercept form of a line, i.e., (y = mx + b), to obtain the line's equation.