Drawing Straight Line Graphs

To find the missing value, substitute the given values into the equation.

When $x = -1$, we get $y = dfrac{1}{2} times (-1) + 5 = 4.5$

When $x = 2$, we get $y = dfrac{1}{2} times (2) + 5 = 6$

When $y = 7$, we get $7 = dfrac{1}{2}x + 5$

Subtract $5$ from both sides of this equation to get

$2 = dfrac{1}{2}x$

Multiplying both sides by $2$, we immediately get $x = 4$. The completed table looks like:

Plotting these points and using them to draw the graph should look like:

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Let’s rearrange this equation. Subtract $1$ from both sides:

$2y = 8x – 1$

Then, divide both sides by $2$:

$y = 4x – dfrac{1}{2}$

So, the $y$-intercept is $-frac{1}{2}$, and the gradient is $4$ – so each time $x$ increases by $1$, $y$ increases by $4$.

This is enough information to draw the graph. The result should look like the figure below.

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Rearranging this equation to be in the form $y = mx +c$, by adding $0.5$ to both sides,

$y = -0.5x + 0.5$

So, the $y$-intercept is $dfrac{1}{2}$, and the gradient is $-dfrac{1}{2}$ – so each time $x$ increases by $1$, $y$ decreases by $0.5$

The result should look like the figure below.

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We can rearrange this equation by subtracting $2$ from both sides:

$2y = 3x – 2$

Then, dividing both sides by $2$:

$y = dfrac{3}{2}x – 1$

So, the $y$-intercept is $-1$, and the gradient is $dfrac{3}{2}$ – so each time $x$ increases by $1$, $y$ increases by $1.5$

The result should look like the figure below.

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We can rearrange this equation by subtracting $4x text{ and } 2$ from both sides:

$y = -4x – 2$

So, the $y$-intercept is $-2$, and the gradient is $-4$ – so each time $x$ increases by $1$, $y$ decreases by $4$

The result should look like the figure below.

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