Question(9) Tick the equations that are straight line graphs. $\begin{array}{ll} y=6-x & \square=5+x^{2} \square \\ y=3+\frac{x}{2} \quad \square & y=2 x+3 \end{array}$

Studdy Solution

STEP 1

1. A straight line graph is represented by a linear equation in the form $y = mx + c$ , where $m$ and $c$ are constants.
2. We need to identify which of the given equations fit this linear form.

STEP 2

1. Identify the form of each equation.
2. Determine if each equation is a linear equation.
3. Tick the equations that are linear.

STEP 3

Identify the form of each equation:
1. $y = 6 - x$
2. $= 5 + x^2$
3. $y = 3 + \frac{x}{2}$
4. $y = 2x + 3$

STEP 4

Determine if each equation is a linear equation:
1. $y = 6 - x$ is in the form $y = -x + 6$ , which is linear.
2. $= 5 + x^2$ is not in the form $y = mx + c$ because of the $x^2$ term, which makes it non-linear.
3. $y = 3 + \frac{x}{2}$ is in the form $y = \frac{1}{2}x + 3$ , which is linear.
4. $y = 2x + 3$ is in the form $y = 2x + 3$ , which is linear.

STEP 5

Tick the equations that are linear:
1. $y = 6 - x$ $\checkmark$
3. $y = 3 + \frac{x}{2}$ $\checkmark$
4. $y = 2x + 3$ $\checkmark$
The equations that are straight line graphs are: - $y = 6 - x$ - $y = 3 + \frac{x}{2}$ - $y = 2x + 3$

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