This graph shows part of a straight line - OCR - GCSE Maths - Question 22 - 2020 - Paper 1

The gradient (m) of a line can be calculated using the formula:

$m = \frac{\text{change in } y}{\text{change in } x}$

Considering two points on the line, for example (0, 5) and (2, 1):

• Change in y: 1 - 5 = -4
• Change in x: 2 - 0 = 2

Thus,

$m = \frac{-4}{2} = -2$

Therefore, the gradient of the line is -2.

The equation of a straight line can be expressed in the form:

$y = mx + c$

Using the gradient m = -2 and the y-intercept c = 5, the equation becomes:

$y = -2x + 5$.

To determine if the line passes through the point (50, -103), substitute x = 50 into the line equation:

$y = -2(50) + 5$

Calculating this gives:

$y = -100 + 5 = -95$

Since -95 does not equal -103, the line does not pass through the point (50, -103). Therefore, the answer is:

no, it will not pass through that point because substituting x = 50 gives y = -95.