1. The equation of the line, which has a gradient of, $ - 5$ is

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The question asks for the equation of a line that has a gradient (slope) of -5.

First, recall that a line with slope m can be written in slope-intercept form as y = mx + b, where b is the y-intercept. For m = -5, this becomes y = -5x + b, which corresponds to all lines with slope -5.

Alternatively, in standard form Ax + By = C, a line with slope -5 can be written as 5x + y = C. Any equivalent equation obtained by multiplying both sides by a nonzero constant will still represent the same slope.

If an option is of the form 10x + 2y = 12, we can simplify by dividing every term by 2 to get 5x + y = 6. This is indeed in standard form with slope -5, because solving for y gives y = -5x + 6.

Now, since the provided data shows only one given option: 'b. 10x + 2y = 12', we evaluate its validity. Dividing by 2 yields 5x + y = 6, which has slope -5 when rearranged to y = -5x + 6. Thus, this equation satisfies the required gradient of -5.

If there were other options, we would assess them similarly: any equation equivalent to y = -5x + b or 5x + y = b would be correct; any equation that, when solved for y, does not yield a coefficient of -5 for x would be incorrect.

In summary, the line with slope -5 can be represented by y = -5x + b or equivalently 5x + y = b; the specific form 10x + 2y = 12 simplifies to 5x + y = 6, which indeed has slope -5.

MCD1550 / MCD2140 - T1 - 2025 TEST 1 (Week 4)

1. The equation of the line, which has a gradient of, \( - 5\) is

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