For the linear equation: 10x−2y=410x-2y=4

gradient = [Fill in the blank],

y-intercept = [Fill in the blank],

Question

For the linear equation:      10x−2y=410x-2y=4

gradient = [Fill in the blank],

y-intercept = [Fill in the blank],

BlackTom AI · Accepted Answer

We are given the linear equation in standard form: 10x − 2y = 4. To find the gradient (slope) and the y-intercept, it’s helpful to solve for y in terms of x and rewrite the equation in slope-intercept form, y = mx + b.

Step 1: Solve for y.
- Start with 10x − 2y = 4.
- Subtract 10x from both sides: −2y = 4 − 10x.
- Divide every term by −2: y = (4 − 10x)/−2 = (−4/2) + (10x/2) = −2 + 5x.
- Rearranging gives y = 5x − 2.

Step 2: Identify the gradient (slope) and y-intercept from the slope-intercept form y = mx + b.
- The coefficient of x is the slope m. Here, m = 5, so the gradient is 5.
- The constant term b is the y-intercept, which is the value of y when x = 0. Here, b = −2, so the y-intercept is −2.

Rationale check: If x = 0, the equation becomes 10(0) − 2y = 4 → −2y = 4 → y = −2, which matches the y-intercept found. If we increase x by 1 unit, y increases by 5 units in accordance with the slope 5, confirming consistency with the slope-intercept form.

For the linear equation: 10x−2y=410x-2y=4 gradient = [Fill in the blank], y-intercept = [Fill in the blank],

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