Properties of a Straight Line
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2 Consider the straight line $y = mx + c$ where $m \neq 0$. a Copy and complete the table of values alongside. b Write down the axes intercepts of the straight line. c i Find the x-step and y-step between the points with x-coordinates 0 and 2. ii Hence find the gradient of the line. d Copy and complete: A straight line with equation $y = mx + c$ has gradient ...... and y-intercept ......
This question includes visual content: The image includes a table with two rows. The top row (x-values) contains: -2, 0, 2, and -c/m. The bottom row (y-values) is empty, waiting to be filled. The text surrounds this table.
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Hi Melek, let's explore the properties of a linear equation by working through these steps for the general form y equals m x plus c.
Linear Functions
Equation: $y = mx + c$
For part a, we need to complete the table of values using the equation. Let's start with x equals negative two.
Next, when x equals zero, the term m x disappears, leaving us with y equals c.
When x equals two, y becomes two m plus c.
Finally, when x equals negative c over m, the m's cancel out, resulting in negative c plus c, which is zero.
Here is our completed table.
| x | -2 | 0 | 2 | -\frac{c}{m} |
|---|---|---|---|---|
| y | -2m+c | c | 2m+c | 0 |
Now for part b, let's identify the axes intercepts. The y-intercept occurs when x is zero.
Axes Intercepts
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